Applications – Science and Engineering

GLOBAL CONVERGENCE OF AN ELASTIC MODE APPROACH FOR A CLASS OF MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Mechanical Engineering Tags , , ,

    We prove that any accumulation point of an elastic mode approach, applied to the optimization of a mixed P variational inequality, that approximately solves the relaxed subproblems is a C-stationary point of the problem of optimizing a parametric mixed P variational inequality. If, in addition, the accumulation point satis es the MPCC-LICQ constraint quali cation and if … Read more

    A direct formulation for sparse PCA using semidefinite programming

  • Alexandre d'Aspremont
  • Laurent El Ghaoui
  • Michael I. Jordan
  • G. R. G. Lanckriet
    • Categories Finance and Economics, Semi-definite Programming, Statistics Tags , ,

    We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem arises in the decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology to finance. We use a modification … Read more

    Constrained optimization in seismic reflection tomography: an SQP augmented Lagrangian approach

  • Frederic Delbos
  • Jean Charles Gilbert
  • R. Glowinski
  • D. Sinoquet
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Quadratic Programming Tags , , , , , ,

    Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a nonlinear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori … Read more

    Fuzzy Modeling with Adaptive Simulated Annealing

  • Hime Aguiar e Oliveira Jr.
    • Categories Control Applications, Global Optimization Applications

    A new method for data-based fuzzy system modeling is presented. The approach uses Takagi-Sugeno models and Adaptive Simulated Annealing (ASA) to achieve its goal . The problem to solve is well defined – given a training set containing a finite number of input-output pairs, construct a fuzzy system that approximates the behavior of the real … Read more

    Construction project scheduling problem with uncertain resource constraints

  • Tang Guochun
  • Zhong-Ping Wan
  • Julin He
    • Categories Applications - Science and Engineering, Scheduling

    This paper discusses that major problem is the construction project scheduling mathematical model and a simple algorithm in the uncertain resource environments. The project scheduling problem with uncertain resource constraints comprised mainly three parties: one of which its maximal limited capacity is fixed throughout the project duration; second maximal limited resource capacity is random variable; … Read more

    Inherent smoothness of intensity patterns for intensity modulated radiation therapy generated by simultaneous projection algorithms

  • Yair Censor
  • James M. Galvin
  • Darek Michalski
  • Ying Xiao
    • Categories Biomedical Applications, Convex Optimization Tags , , , ,

    The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumor as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighboring intensities. Accurately … Read more

    Pointillism via Linear Programming

  • Robert Bosch
  • Adrianne Herman
    • Categories Airline Optimization, Applications - Science and Engineering, Linear Programming Tags ,

    Pointillism is a painting technique in which the painter places dots of paint on the canvas in such a way that they blend together into desired forms when viewed from a distance. In this brief note, we describe how to use linear programming to construct a pointillist portrait. CitationDept. of Mathematics, Oberlin College, Oberlin, OH … Read more

    Implementation of Infinite Dimensional Interior Point Method for Solving Multi-criteria Linear-Quadratic Control Problem

  • Leonid Faybusovich
  • Takashi Tsuchiya
  • Thanasak Mouktonglang
    • Categories Control Applications, Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We describe an implementation of an infinite-dimensional primal-dual algorithm based on the Nesterov-Todd direction. Several applications to both continuous and discrete-time multi-criteria linear-quadratic control problems and linear-quadratic control problem with quadratic constraints are described. Numerical results show a very fast convergence (typically, within 3-4 iterations) to optimal solutions CitationPreprint, May, 2004, University of Notre DameArticleDownload … Read more

    On the Relationship between Bilevel Decomposition Algorithms and Direct Interior-Point Methods

  • Victor DeMiguel
  • Francisco Javier Nogales
    • Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization Tags , , ,

    Engineers have been using \emph{bilevel decomposition algorithms} to solve certain nonconvex large-scale optimization problems arising in engineering design projects. These algorithms transform the large-scale problem into a bilevel program with one upper-level problem (the master problem) and several lower-level problems (the subproblems). Unfortunately, there is analytical and numerical evidence that some of these commonly used … Read more

    A Local Convergence Analysis of Bilevel Decomposition Algorithms

  • Victor DeMiguel
  • Walter Murray
    • Categories Multidisciplinary Design Optimization, Nonlinear Optimization Tags , , ,

    Decomposition algorithms exploit the structure of large-scale optimization problems by breaking them into a set of smaller subproblems and a coordinating master problem. Cutting-plane methods have been extensively used to decompose convex problems. In this paper, however, we focus on certain nonconvex problems arising in engineering. Engineers have been using bilevel decomposition algorithms to tackle … Read more